In this paper, we calculated the conversion factor \(c_B^{\rm win}\)  as a function of the leptogenesis temperature \(T_{B-L}\) , in five separate temperature regimes, and in dependence of the number of active lepton flavors participating in the dynamics of wash-in leptogenesis (see Tab. REF ).
These results significantly extend our previous results in Ref. [1]} and provide a consistent treatment of coherence / decoherence as well as heavy-neutrino flavor effects.
Equipped with the coefficients listed in Tab. REF , we were then able to identify the viable regions in the two-dimensional parameter space spanned by \(\chi \)  and the reheating temperature \(T_{\rm rh}\)  (see Fig. REF ).
A priori, one may worry that the global charges in Eq. (REF ) could be erased by magnetic diffusion or the chiral plasma instability soon after inflation.
Based on rough estimates of the diffusion temperature \(T_{\rm diff}\)  [see Eq. (REF )], the magnetic Reynolds number [see Eqs. (REF ) and ()], and the CPI temperature \(T_{\rm CPI}\)  [see Eq. (REF )], we, however, argued that baryogenesis after axion inflation typically takes place in parameter regions that are spared from these two phenomena.
Magnetic diffusion might become an issue, according to our less optimistic estimate of the magnetic Reynolds number; but even in this case, a large temperature window for successful wash-in leptogenesis remains (see the two plots in the right column of Fig. REF ).
In the absence of heavy RHNs, one would have to conclude in this case that baryogenesis after axion inflation does not succeed in explaining the observed BAU, i.e., there is no contribution to the BAU from baryogenesis via helicity decay.
However, adding RHNs with masses above \(M_1^{\rm min} \sim 10^{8\cdots 9}\,\textrm {GeV}\)  to the SM particle content can rescue these scenarios.
